To solve this equation, we can expand the expression on the left side:

X(x+4)(x+4) = 0
X(x^2 + 4x + 4x + 16) = 0
X(x^2 + 8x + 16) = 0

Now, we have a quadratic equation in the form of X(x^2 + 8x + 16) = 0. To solve for X, we can set each factor equal to zero:

X = 0
x^2 + 8x + 16 = 0

To solve the quadratic equation above, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = 1, b = 8, and c = 16. Substituting these values into the formula:

x = (-8 ± √(8^2 - 4116)) / 2(1)
x = (-8 ± √(64 - 64)) / 2
x = (-8 ± √0) / 2
x = (-8 ± 0) / 2
x = -8 / 2
x = -4

Therefore, the solutions to the equation X(x+4)(x+4) = 0 are X = 0 and x = -4.